1. Field of the Invention
This invention relates in general to vertical-scanning interferometric (VSI) techniques for surface characterization. In particular, it relates to a new method for combining information about the peak of the envelope and the phase of a VSI correlogram.
2. Description of the Related Art
Optical surface profilometry enables the performance of non-contact measurements of fragile surfaces with high resolution and at high measurement speeds. Several widely accepted techniques are available for calculating surface topography from optical interference data.
Phase-shifting interferometry (PSI), for example, is based on changing the phase difference between two coherent interfering beams at a single wavelength, λ, in some known manner, for example by changing the optical path difference (OPD) either continuously or discretely with time. Several measurements of light intensity with different OPD values, usually equally spaced, at a pixel of a photodetector can be used to determine the phase difference between the interfering beams at the point on a test surface corresponding to that pixel. Based on such measurements at all pixels with coordinates (x,y), a phase map Φ(x,y) of the test surface can be obtained, from which very accurate data about the surface profile may be obtained using well known algorithms.
PSI provides a vertical resolution on the order of 1/1000 of a wavelength or better; thus, it is well suited for characterizing smooth, well-reflecting surfaces. At the same time, the PSI technique has a limited vertical range of application because of the so-called 2π ambiguity; i.e., the fact that the phase shift between two beams is repeated with 2π periods every time the OPD exceeds a distance of λ/2. This “phase wrapping” behavior of PSI leads to ambiguity in the measurements of the surface profile when the surface features are higher than λ/2. Thus, in practice, conventional PSI techniques have been limited to measurements of fairly smooth and continuous surfaces because only in such cases can phase-unwrapping algorithms be applied to reconstruct the surface shape.
Large-step, rough, or steep-surface measurements, on the other hand, have been traditionally carried out with white-light (or broadband-light) vertical-scanning interferometry (VSI). As conventionally implemented, VSI uses a white-light source and the reference arm of the interferometer is scanned vertically with respect to a stationary test sample (or vice versa). In VSI, the degree of contrast of fringes produced on the detector by two interfering beams (instead of their phases) is measured as a function of distance between the reference and test surfaces to obtain information about the test surface. The contrast of a VSI interferogram is maximum when the OPD approaches zero, as illustrated in FIG. 1, and the test surface topography may be reconstructed by determining the peak position of the envelope of the interferogram for each detector pixel. The VSI approach overcomes the limited scanning range associated with PSI techniques, but suffers from significantly lower resolution (about 3 nm) and, therefore, is not as precise as PSI.
Together, PSI and VSI make it possible to measure most samples. However, they do not allow measurement of samples that combine smooth surfaces with large profile gradients. Measuring the profile discontinuities of such samples requires the large scanning range of VSI, while characterizing a smooth surface texture requires a PSI resolution. This problem has been recently addressed by the development of an enhanced VSI algorithm (named EVSI in the art) that combines both PSI and VSI. As illustrated in FIG. 2, the EVSI algorithm involves two sequential steps. First, a series of frames, spaced approximately □/8 apart, is captured as the test surface is scanned through focus (OPD=0) in VSI mode and a coarse height is calculated by determining the frame position closest to the peak of the envelope of the correlogram (Imax). Once the peak frame position is found, a series of frames around the peak frame (frames 1 through 5 in the figure) is used in conventional PSI mode to acquire phase data in the proximity of the peak frame. By combining these two sets of data, the height of each point of the surface is determined with sub-nanometer resolution over the entire scanning range of the VSI profilometer.
However, the EVSI technique is limited in several aspects. First, conventional PSI n-frame algorithms are very sensitive to phase-step errors between scan frames. Small random errors in the frame step (such as due to scanner error or vibration, for example) can cause significant noise on the calculated phase map, such as the so-called fringe print-through error. Second, since the phase is determined from a series of frames around the peak frame of the correlogram's envelope, the phase at each pixel depends on the peak frame position for the pixel. Thus, the signal-to-noise ratio of the phase map is deteriorated by the uncertainty associated with defining frame positions with respect to the peak of each envelope. In other words, all errors present in the calculation of the VSI coarse map are propagated to the PSI phase map (therefore, it is difficult to obtain independent high-resolution or PSI-like phase maps). Third, for high-speed scanning where frames are acquired at a phase step (also referred to herein as the scan step) of (2n+1)π/2 (where n=1, 2, 3 . . . ), the error accumulated in the frame positions using EVSI can be significant. Fourth, the fact that the calculation of phase data can be carried out only after acquisition of all frame data and calculation of the peak of the envelope data requires storing of all frame data until all calculations have been completed at the end of the scan, which limits real-time data processing capabilities and causes undesirable issues related to measurement throughput and limitations in computer memory requirements.
Therefore, it would be desirable to be able to combine VSI-scan data with a phase map of the surface obtained independently of the peak of the VSI envelope. It would also be desirable to determine the phase map in real time, simultaneously with the calculation of the VSI coarse surface-height profile. The present invention addresses this need by providing a method for handling conventional VSI-scan data that affords low-noise mapping with sub-nanometer resolution across a large scanning range. The method of the invention, called high-definition vertical-scan interferometry (hereinafter referred to as HDVSI), enables the determination of both the peak of the envelope and the phase of the correlogram in real time with calculations that are independent from one another. Also, the phase of the correlogram is determined based on cumulative data (i.e., based on all frames and independent of scanner position), which provides an additional advantage with respect to the prior art.